The onset of electrothermoconvection in a rotating Brinkman porous layer

Abstract

The criterion for the onset of electrothermoconvection in a rotating horizontal layer of Brinkman porous medium is investigated for different types of velocity boundary conditions namely, (i) both boundaries stress-free, (ii) both boundaries rigid and (iii) lower rigid and upper free boundaries. Results indicate that the nature of boundaries and speed of rotation significantly influence the stability characteristics of the system. In the case of stress-free condition, it is shown that the necessary conditions for the occurrence of oscillatory onset are independent of an external electric field. Contrary to their stabilizing effect in the absence of rotation, increasing the ratio of viscosities Λ and decreasing the Darcy number Da show some destabilizing effect on the onset of stationary electrothermoconvection in the presence of rotation and some important observations are made on the stability characteristics of the system. Moreover, the similarities and differences between free–free, rigid–rigid and rigid–free boundaries are emphasized in triggering the onset of electrothermoconvection in a rotating porous layer. For small Taylor number domain, the stress-free boundaries is found to be always unstable than that of rigid–rigid and rigid–free boundaries. However, this trend is reversed at higher Taylor number domain because the stability of the stress-free case is increased more quickly than the other boundaries.